A unified model for the structure of polymers in semidilute solution

Pressure of Linear and Ring Polymers Confined in a Cavity

Nanoscale confinement of polymers in a cavity is central to a variety of biological and nanotechnology processes. Using the discrete WLC model we simulate the compression of flexible and semiflexible polymers of linear and ring topology in a closed cavity. Simulation reveals that polymer pressure inside the cavity increases with the chain stiffness but is practically unaffected by the chain topology. For flexible polymers, the computed dependence of pressure on the cavity size and polymer concentration is consistent with the scaling behavior expected for bulk polymers in a good solvent. However, the scaling behavior of semiflexible polymers is only in partial agreement with the theory prediction, with discrepancies arising from a continuous transition between regimes in chains of moderate lengths. The computed segment density profiles endorse the propensity of semiflexible polymers to concentrate beneath the cavity surface and thus elevate the pressure. The compaction of polymers by compression into the disordered globule or growing toroidal structure is documented.

Mathematical modelling of cross-linked polyacrylic-based hydrogels: physical properties and drug delivery

Recently, hydrogels have gained significant importance in different applications, such as tissue engineering and drug delivery. They are 3D structures of hydrophilic polymers held together through physical or chemical crosslinking. Important is their ability to swell in presence of solvents, forming elastic gels able to maintain their original shape. Furthermore, these scaffolds slowly degrade in the physiological environment, leading the growing tissue to replace the former filled site. In this work, hydrogels have been synthetized using branched polyacrylic acid (carbomer) cross-linked with an aliphatic polyetherdiamine (elastamine). In particular, we focused on the description of their equilibrium conditions in swollen state and the dynamic simulation of the swelling process. These hydrogels exhibited a peculiar swelling behaviour characterized by an overshoot of the volume increase before reaching the equilibrium. Notably, such behaviour was found at different pH values. In this manuscript, the swelling behaviour was studied by mathematical modelling. Moreover, the ability of these devices to release drugs was also examined through a literature model to understand the different operating transport mechanisms.

Impact of the protein composition on the structure and viscoelasticity of polymer-like gluten gels

We investigate the structure of gluten polymer-like gels in a binary mixture of water/ethanol, 50/50 v/v, a good solvent for gluten proteins. Gluten comprises two main families of proteins, monomeric gliadins and polymer glutenins. In the semi-dilute regime, scattering experiments highlight two classes of behavior, akin to standard polymer solution and polymer gel, depending on the protein composition. We demonstrate that these two classes are encoded in the structural features of the proteins in very dilute solution, and are correlated with the presence of proteins assemblies of typical size tens of nanometers. The assemblies only exist when the protein mixture is sufficiently enriched in glutenins. They are found directly associated to the presence in the gel of domains enriched in non-exchangeable H-bonds and of size comparable to that of the protein assemblies. The domains are probed in neutron scattering experiments thanks to their unique contrast. We show that the sample visco-elasticity is also directly correlated to the quantity of domains enriched in H-bonds, showing the key role of H-bonds in ruling the visco-elasticity of polymer gluten gels.

Macromolecular diffusion in crowded media beyond the hard-sphere model

The effect of macromolecular crowding on diffusion beyond the hard-core sphere model is studied. A new coarse-grained model is presented, the Chain Entanglement Softened Potential (CESP) model, which takes into account the macromolecular flexibility and chain entanglement. The CESP model uses a shoulder-shaped interaction potential that is implemented in the Brownian Dynamics (BD) computations. The interaction potential contains only one parameter associated with the chain entanglement energetic cost (Ur). The hydrodynamic interactions are included in the BD computations via Tokuyama mean-field equations. The model is used to analyze the diffusion of a streptavidin protein among different sized dextran obstacles. For this system, Ur is obtained by fitting the streptavidin experimental long-time diffusion coefficient Dlongversus the macromolecular concentration for D50 (indicating their molecular weight in kg mol-1) dextran obstacles. The obtained Dlong values show better quantitative agreement with experiments than those obtained with hard-core spheres. Moreover, once parametrized, the CESP model is also able to quantitatively predict Dlong and the anomalous exponent (α) for streptavidin diffusion among D10, D400 and D700 dextran obstacles. Dlong, the short-time diffusion coefficient (Dshort) and α are obtained from the BD simulations by using a new empirical expression, able to describe the full temporal evolution of the diffusion coefficient.

Near-second-order transition in confined living-polymer solutions

We analyze a near-second-order transition occurring in solutions of living polymers confined by two parallel surfaces in equilibrium with a reservoir solution. The molecular self-consistent field theory in the regime of weak adsorption or depletion is mapped to phenomenological Landau theory, where the order parameter is the average degree of polymerization or, equivalently, the normalized chain-end concentration. The distance between two surfaces at which the transition occurs scales as ℓ(c)(2)|c| where ℓ(c) is the correlation length of the polymer solution in the reservoir and c(-1) is de Gennes adsorption length. In the second half of the paper we focus on experimentally observable features. The predicted transition can be detected experimentally by probing the living-polymer mediated disjoining potential between surfaces by means of, e.g., colloidal probe atomic force microscopy. To facilitate experimental investigations we derive simple explicit expressions for the disjoining potential for several regimes. By comparison with full numerical calculations it was verified that these are quite accurate.

An assessment of the ability of the obstruction-scaling model to estimate solute diffusion coefficients in hydrogels

The ability to estimate the diffusion coefficient of a solute within hydrogels has important application in the design and analysis of hydrogels used in drug delivery, tissue engineering, and regenerative medicine. A number of mathematical models have been derived for this purpose; however, they often rely on fitted parameters and so have limited predictive capability. Herein we assess the ability of the obstruction-scaling model to provide reasonable estimates of solute diffusion coefficients within hydrogels, as well as the assumption that a hydrogel can be represented as an entangled polymer solution of an equivalent concentration. Fluorescein isothiocyanate dextran solutes were loaded into sodium alginate solutions as well as hydrogels of different polymer volume fractions formed from photoinitiated cross-linking of methacrylate sodium alginate. The tracer diffusion coefficients of these solutes were measured using fluorescence recovery after photobleaching (FRAP). The measured diffusion coefficients were then compared to the values predicted by the obstruction-scaling model. The model predictions were within ±15% of the measured values, suggesting that the model can provide useful estimates of solute diffusion coefficients within hydrogels and solutions. Moreover, solutes diffusing in both sodium alginate solutions and hydrogels were demonstrated to experience the same degree of solute mobility restriction given the same effective polymer concentration, supporting the assumption that a hydrogel can be represented as an entangled polymer solution of equivalent concentration.

Formulation of in situ chemically cross-linked hydrogel depots for protein release: from the blob model perspective

The fast release rate and the undesirable covalent binding are two major problems often encountered in formulating in situ chemically cross-linked hydrogel as protein release depot, particularly when prolonged release over months is desirable. In this study, we applied the De Gennes' blob theory to analyze and tackle these two problems using a vinylsulfone-thiol (VS-SH) reaction based in situ hydrogel system. We showed that the simple scaling relation ξb ≈ Rg(c/c*)(-v/(3v-1)) is applicable to the in situ hydrogel and the mesh size estimated from the precursor polymer parameters is a reasonable match to experimental results. On the other hand, as predicted by the theory and confirmed by experiments, the drug diffusion within hydrogel depends mainly on polymer concentration but not the degree of modification (DM). The covalent binding was found to be caused by the mismatch of location between the reactive groups and the entanglement points. The mismatch and, thus, the protein binding were minimized by increasing the DM and concentration of the SH polymer relative to the VS polymer, as predicted by theory. Using these principles, an in situ hydrogel system for the controlled release of an antiangiogenic antibody therapeutics bevacizumab for 3 months was developed.

Structure of Soluble Silicates

Small angle x-ray scattering (SAXS) is the technique of choice for the determination of structure on the 10–1000Å scale. We have used this technique to study the growth and topology of the macromolecules which precede gelation in several chemical systems used in sol-gel glass technology. The results show that branched polymers, as opposed to colloids, are formed. The alcoholic silica system is akin to organic systems where gelation occurs through growth and crosslinking of chain molecules. Data are reported from both the Porod and Guinier regions of the SAXS curve and these data are interpreted in terms of geometrical structures predicted by various disorderly growth processes. The results indicate that the degree of crosslinking can be controlled by catalytic conditions. The degree of crosslinking may, in turn, control phase separation and processability to a dense glass.

Hindered Diffusion of Oligosaccharides in High Strength Poly(ethylene glycol)/Poly(acrylic acid) Interpenetrating Network Hydrogels: Hydrodynamic Versus Obstruction Models

Diffusion coefficients of small oligosaccharides within high strength poly(ethylene glycol)/poly(acrylic acid) interpenetrating network (PEG/PAA IPN) hydrogels were measured by diffusion through hydrogel slabs. The ability of hindered diffusion models previously presented in the literature to fit the experimental data is examined. A model based solely on effects due to hydrodynamics is compared to a model based solely on solute obstruction. To examine the effect of polymer volume fraction on the observed diffusion coefficients, the equilibrium volume fraction of polymer in PEG/PAA IPNs was systematically varied by changing the initial PEG polymer concentration in hydrogel precursor solutions from 20 to 50 wt./wt.%. To examine the effect of solute radius on the observed diffusion coefficients, solute radii were varied from 3.3 to 5.1 Å by measuring diffusion coefficients of glucose, a monosaccharide; maltose, a disaccharide; and maltotriose, a trisaccharide. Both the hydrodynamic and obstruction models rely on scaling relationships to predict diffusion coefficients. The proper scaling relationship for each of the hindered diffusion models is evaluated based on fits to experimental data. The scaling relationship employed is found to have a greater significance for the hydrodynamic model than the obstruction model. Regardless of the scaling relationship employed, the obstruction model provides a better fit to our experimental data than the hydrodynamic model.

Flexible chain molecules in the marginal and concentrated regimes: universal static scaling laws and cross-over predictions

We present predictions for the static scaling exponents and for the cross-over polymer volumetric fractions in the marginal and concentrated solution regimes. Corrections for finite chain length are made. Predictions are based on an analysis of correlated fluctuations in density and chain length, in a semigrand ensemble in which mers and solvent sites exchange identities. Cross-over volumetric fractions are found to be chain length independent to first order, although reciprocal-N corrections are also estimated. Predicted scaling exponents and cross-over regimes are compared with available data from extensive off-lattice Monte Carlo simulations [Karayiannis and Laso, Phys. Rev. Lett. 100, 050602 (2008)] on freely jointed, hard-sphere chains of average lengths from N=12-500 and at packing densities from dilute ones up to the maximally random jammed state.

Investigation of the Structure of Cellulose in LiCl/DMAc Solution and Its Gelation Behavior by Small-Angle X-Ray Scattering Measurements

Cellulose gels were prepared from cellulose in lithium chloride/N,N-dimethylacetamide (LiCl/DMAc) solution. When the cellulose concentration in the solution is above the one at which cellulose molecules overlap, cellulose gels were formed. While the gel prepared by the addition of water was turbid, the one prepared by the ion exchange was colorless, transparent, and optically anisotropic. In order to explain this gelation behavior of cellulose, small-angle X-ray scattering (SAXS) measurements of the cellulose solutions and the gels were performed. The SAXS profiles of the cellulose solutions and the gels suggested that the large-scale fluctuation of the molecular chain density in the solution can be the origin of the molecular aggregates formed in the gel. Furthermore, the differences in the structure of the gels at the macroscopic and the molecular level were discussed in terms of the phase separation and the molecular association.

Anomalous diffusion of proteins due to molecular crowding

We have studied the diffusion of tracer proteins in highly concentrated random-coil polymer and globular protein solutions imitating the crowded conditions encountered in cellular environments. Using fluorescence correlation spectroscopy, we measured the anomalous diffusion exponent alpha characterizing the dependence of the mean-square displacement of the tracer proteins on time, r(2)(t) approximately t(alpha). We observed that the diffusion of proteins in dextran solutions with concentrations up to 400 g/l is subdiffusive (alpha < 1) even at low obstacle concentration. The anomalous diffusion exponent alpha decreases continuously with increasing obstacle concentration and molecular weight, but does not depend on buffer ionic strength, and neither does it depend strongly on solution temperature. At very high random-coil polymer concentrations, alpha reaches a limit value of alpha(l) approximately 3/4, which we take to be the signature of a coupling between the motions of the tracer proteins and the segments of the dextran chains. A similar, although less pronounced, subdiffusive behavior is observed for the diffusion of streptavidin in concentrated globular protein solutions. These observations indicate that protein diffusion in the cell cytoplasm and nucleus should be anomalous as well, with consequences for measurements of solute diffusion coefficients in cells and for the modeling of cellular processes relying on diffusion.

Power laws in polymer solution dynamics

The dynamical screening length xi(h) in semidilute to highly concentrated polymer solutions of poly(methyl methacrylate) in propylene carbonate has been examined using photon correlation spectroscopy and pulsed field gradient nuclear magnetic resonance. A crossover between different concentration dependent regimes, xi(h) approximately phi(-alpha), where alpha is found to be approximately 0.5, approximately 1, and approximately 2, is observed when the local viscosity is taken into account. Here phi is the volume fraction of polymer in the solution. Well-defined crossovers between alpha=0.5 and alpha=1 corresponding to a transition from a marginal solvent to a theta solvent behavior have been predicted to occur due to the reduction of excluded-volume effects between the spatially correlated polymer segments with increasing polymer volume fraction. However, a clear experimental validation of the crossover has never been presented before. The third regime (alpha approximately 2) is observed in the highly concentrated region where the static screening length is comparable to the persistence length of the polymer. The observation indicates that the rigid rod model previously used to describe concentrated solutions is an oversimplification valid only in the very high concentration limit. The obtained results at high concentrations are discussed in the frame of a simple physical model where segments at the persistence length scale are treated as flexible rodlike segments.

Correlation between mesh size and equilibrium degree of swelling of polymeric networks

A correlation is established between the mesh size of a swollen cross-linked network and its equilibrium polymer volume fraction, for hydrogels isothermally swollen up to semidilute, dilute, or concentrated conditions. The exponent of this correlation decreases as the water concentration of the hydrogel decreases. Experimental results with hydrogels of poly(vinyl alcohol) and poly(2-hydroxy ethyl methacrylate) are used to verify the new scaling laws.